algebra
Polynomial Operations
January 17, 2026
6 min read
PanMaths Team
Adding Polynomials
Combine like terms โ terms with the same variable and exponent.
(3xยฒ + 2x + 1) + (xยฒ - 4x + 5)= 4xยฒ - 2x + 6
Subtracting Polynomials
Distribute the negative, then combine like terms.
(5xยฒ + 3x - 2) - (2xยฒ - x + 4)= 5xยฒ + 3x - 2 - 2xยฒ + x - 4
= 3xยฒ + 4x - 6
Multiplying Polynomials (FOIL)
For binomials: First, Outer, Inner, Last
(x + 2)(x + 3)= xยทx + xยท3 + 2ยทx + 2ยท3
= xยฒ + 3x + 2x + 6
= xยฒ + 5x + 6
๐กLike Terms Quick Check
3xยฒ and 5xยฒ are like terms (same variable, same exponent). 3xยฒ and 3x are NOT like terms (different exponents). Always match both the variable AND the exponent!
โ ๏ธ Common Mistakes
- Adding exponents when adding terms (wrong!): 3xยฒ + 2xยฒ โ 5xโด
- Forgetting to distribute the negative sign to all terms
- Missing terms when using FOIL โ check you have 4 products!
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